INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS
A solar cell system integrated with a conductive polymer composite fuse (CPCF) for passive protection against hot spot formation was numerically investigated. The model, based on differential heat balance equations, simulates diurnal temperature and power dynamics for Stony Brook, NY, on September 3...
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| author | Korsunskyi , R. Nakashydze, L. |
| author_facet | Korsunskyi , R. Nakashydze, L. |
| author_institution_txt_mv | [
{
"author": "R. Korsunskyi ",
"institution": "The Stony Brook School, New York, USA"
},
{
"author": " L. Nakashydze",
"institution": "Oles Honchar Dnipro National University, Research Institute of Energy-Efficient Technologies and Materials Science, Dnipro, Ukraine"
}
] |
| author_sort | Korsunskyi , R. |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:22Z |
| description | A solar cell system integrated with a conductive polymer composite fuse (CPCF) for passive protection against hot spot formation was numerically investigated. The model, based on differential heat balance equations, simulates diurnal temperature and power dynamics for Stony Brook, NY, on September 3rd, when the fuse is in the high-conductivity state, by considering heat exchange between the solar cell and the CPCF under varying solar irradiance and ambient conditions. Key material and structural parameters—such as thermal contact resistance, CPCF thickness, activation energy, percolation pre-exponential factor, and transition exponent—are varied to evaluate their influence on system performance. Results demonstrate that thermal contact resistance significantly influences temperature distribution between components without substantially affecting power output, while electrical parameters such as activation energy and percolation constants significantly influence power dissipation and overall energy loss. The findings provide a framework for optimizing CPCF design to enhance solar cell reliability and efficiency, offering a cost-effective, passive alternative to conventional hotspot mitigation methods.  |
| doi_str_mv | 10.36296/1819-8058.2025.3(82).115-124 |
| first_indexed | 2025-10-01T01:30:53Z |
| format | Article |
| fulltext |
115
Відновлювана енергетика. № 3/2025 | Сонячна енергетика
УДК620.91 https://doi.org/10.36296/1819-8058.2025.3(82).115-124
INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES
ON THE EFFICIENCY OF SOLAR CELLS
Received Jun. 09, 2025; accepted Sept. 22, 2025
Available online Sept. 30, 2025
Korsunskyi R.1, Nakashydze L.2
Author for correspondence: Nakashydze Lilia,
e-mail: foton_dnu@ukr.net
Annotation: A solar cell system integrated with a conductive
polymer composite fuse (CPCF) for passive protection against
hot spot formation was numerically investigated. The model,
based on differential heat balance equations, simulates diurnal
temperature and power dynamics for Stony Brook, NY, on September 3rd, when the fuse is in the high-conductivity
state, by considering heat exchange between the solar cell and the CPCF under varying solar irradiance and
ambient conditions. Key material and structural parameters—such as thermal contact resistance, CPCF thickness,
activation energy, percolation pre-exponential factor, and transition exponent—are varied to evaluate their
influence on system performance. Results demonstrate that thermal contact resistance significantly influences
temperature distribution between components without substantially affecting power output, while electrical
parameters such as activation energy and percolation constants significantly influence power dissipation and
overall energy loss. The findings provide a framework for optimizing CPCF design to enhance solar cell reliability
and efficiency, offering a cost-effective, passive alternative to conventional hotspot mitigation methods.
Keywords: solar cell, conductive polymer composite fuse, percolation, nanofiller, polymer matrix.
ВПЛИВ ЕЛЕКТРОТЕПЛОВИХ ПАРАМЕТРІВ ПОЛІМЕРНИХ КОМПОЗИТНИХ ЗАПОБІЖНИКІВ НА
ЕФЕКТИВНІСТЬ СОНЯЧНИХ ЕЛЕМЕНТІВ
Отримано 09 черв. 2025 р.; рекомендовано до публікації 22 вер. 2025 р.
Доступно онлайн 30 вер. 2025 р.
Корсунський Р. Д.1, Накашидзе Л. В. 2
Автор для кореспонденції: Накашидзе Лілія,
e-mail: foton_dnu@ukr.net
Анотація: Було чисельно досліджено сонячний елемент,
інтегрований з провідним полімерно-композитним запо-
біжником для пасивного захисту від утворення гарячих
точок. Математична модель, заснована на диференціа-
льних рівняннях теплового балансу, моделює фізичні про-
цеси в цій системі для Стоуні-Брук, штат Нью-Йорк, 3 вересня, коли запобіжник перебуває у стані висо-
кої провідності, враховуючи теплообмін між сонячною батареєю та запобіжником за змінної сонячної
радіації та умов навколишнього середовища. Ключові параметри матеріалу та конструкції, як-от те-
рмічний контактний опір, товщина матеріалу запобіжника, енергія активації запобіжника, передекс-
поненціальний коефіцієнт перколяції та показник перколяційного переходу, змінюються, щоб оцінити,
як запобіжник впливає на продуктивність системи. Результати демонструють, що термічний конта-
ктний опір суттєво впливає на розподіл температури між компонентами без істотного впливу на
вихідну потужність, тоді як електричні параметри, як-от енергія активації та константи перколяції,
суттєво впливають на розсіювання потужності та загальні втрати енергії. Отримані результати
1 student
https://orcid.org/0009-0001-5361-0641
2 Dr. of Science (Tech.)
https://orcid.org/0000-0003-3990-6718
1 The Stony Brook School, New York, USA
2 Oles Honchar Dnipro National University,
Research Institute of Energy-Efficient
Technologies and Materials Science, Dnipro,
Ukraine
1 студент
https://orcid.org/0009-0001-5361-0641
2 д-р. техн. наук
https://orcid.org/0000-0003-3990-6718
1 Школа Стоуні-Брук, Нью-Йорк, США
2 Дніпровський національний університет
імені Олеся Гончара, Науково-дослідний
інститут енергоефективних технологій
та матеріалознавства, м. Дніпро, Україна
116
Відновлювана енергетика. № 3/2025 | Сонячна енергетика
забезпечують основу для оптимізації конструкції запобіжників для підвищення надійності та ефекти-
вності сонячних елементів, пропонуючи економічно ефективну пасивну альтернативу звичайним ме-
тодам захисту від впливу гарячих точок.
Ключові слова: сонячний елемент, електропровідний полімерно-композитний запобіжник, перколяція,
наповнювач, полімерна матриця.
List of Abbreviations and Symbols
SC – solar cell PVC – photovoltaic cell
CPCF – conductive polymer composite fuse BDF – backwards differentiation formula
Introduction
Interest in renewable energy sources continues to grow
steadily around the world. According to the Global Electricity
Review conducted by the think tank Ember [1], renewable
energy sources supplied a record 30% of the world’s electric-
ity, largely due to the increasing use of solar energy. Various
defects that arise during solar cell (SC) operation lead to mis-
matches in photovoltaic characteristics between individual
SCs and their series-connected groups. As a result, localized
electrical overheating occurs within SCs, known as a "hot
spot," which accelerates degradation processes [2].
In [3], the main causes of SC degradation and failure were
analyzed, identifying hot spots as the source of 22% of
faults. Therefore, one of the key directions for improving
the reliability and efficiency of SCs is the study and devel-
opment of technologies for protection against localized
overheating.
Modern methods of preventing hot spot formation in SCs—
including the use of bypass diodes and various circuit-based
techniques—are not universal. Bypass diodes play a critical
role in preventing mismatch effects, but they lead to tech-
nical challenges such as overheating, replacement needs,
potential failures, and increased manufacturing costs due
to the requirement of multiple diodes per SC series string
[4–6]. Similarly, active bypass switches use field-effect tran-
sistors and can replace conventional bypass diodes, allow-
ing more efficient bypass current flow and significantly re-
ducing voltage drops [7]. In addition, some active detection
systems use thermal images and temperature sensors to
detect hot spots, subsequently activating integrated bypass
switch systems to mitigate them [8]. However, these ad-
vanced methods often result in high costs and significantly
complicate the solar installation.
In [9], a method was proposed for protecting SCs from lo-
calized overheating using a conductive polymer composite
fuse (CPCF) as an embedded layer, maintaining thermal
contact with the SC. In [10], modeling of the electrophysical
characteristics of the system proposed in [9] was carried
out using a polyethylene–carbon nanomaterial as a fuse.
The possibility of applying this model for SC protection was
analyzed, and directions for optimizing fuse parameters in
protection circuits were identified. It was shown that cur-
rently available CPCFs have limited applicability for prevent-
ing localized SC overheating.
A study [11] demonstrated that the melting points of most
commercially produced CPCFs are too high compared to the
maximum operating temperatures of SCs and hot spot con-
ditions. In [12], the possibility of creating CPCFs using a cer-
esin matrix—which has a lower melting point than most
polyesters—combined with carbon black, was presented.
Additionally, current research addresses the temperature
distribution in the proposed model under overvoltage con-
ditions [13]. Theoretical analysis in [13] shows that under
such conditions, the local heating zone of a solar panel ex-
pands over time, causing the posistor layer to heat above
its melting point.
Thus, the limitations and potential advantages of using a
built-in posistor polymer composite layer for electrother-
mal protection of SCs were outlined earlier.
Methods and Results of the Study
To analyze the thermal behavior of a solar cell thermally
coupled with a polymer-composite fuse, a mathematical
model was developed based on a system of first-order dif-
ferential equations describing the temperature dynamics of
both components in thermal contact.
The heat balance for the solar cell is given by:
𝑆𝑠𝐴𝑠𝑞(𝑡) − 𝑆𝑠ℎ𝑠𝜃𝑠(𝑡) −
𝜃𝑠(𝑡)−𝜃𝑝(𝑡)
𝑅𝑠𝑝
= 𝑆𝑠𝜌𝑠𝑐𝑝𝑠𝑙𝑠
𝑑𝜃𝑠(𝑡)
𝑑𝑡
(1)
where: 𝑆𝑠𝐴𝑠𝑞(𝑡) represents heat generation due to solar
irradiance; 𝑆𝑠ℎ𝑠𝜃𝑠(𝑡) is heat loss to the surroundings;
𝜃𝑠(𝑡)−𝜃𝑝(𝑡)
𝑅𝑠𝑝
models heat transfer between the solar cell and
CPCF via thermal resistance 𝑅𝑠𝑝; 𝑆𝑠𝜌𝑠𝑐𝑝𝑠𝑙𝑠
𝑑𝜃𝑠(𝑡)
𝑑𝑡
represents
the heat capacity of the solar cell.
When creating the model, it was assumed that the CPCF
samples consisted of an isotropic mechanical mixture of
polymer matrix and conductive nanofiller.
The heat balance for the polymer-composite fuse is:
𝜃𝑠(𝑡)−𝜃𝑝(𝑡)
𝑅𝑠𝑝
− 𝑆𝑝ℎ𝑝𝜃𝑝(𝑡) + 𝑃(𝑡) = 𝑆𝑝𝜌𝑝𝑐𝑝𝑝𝑙𝑝
𝑑𝜃𝑝(𝑡)
𝑑𝑡
(2)
where: 𝑆𝑝ℎ𝑝𝜃𝑝(𝑡) accounts for heat loss to the surround-
ings;
𝜃𝑠(𝑡)−𝜃𝑝(𝑡)
𝑅𝑠𝑝
represents thermal conduction from the so-
lar cell; 𝑆𝑝𝜌𝑝𝑐𝑝𝑝𝑙𝑝
𝑑𝜃𝑝(𝑡)
𝑑𝑡
describes the heat capacity of the
117
Відновлювана енергетика. № 3/2025 | Сонячна енергетика
CPCF; 𝑃(𝑡) is power dissipation on the layer of the CPCF
due to current flow.
In deriving the heat balance equation for the CPCF, it was
assumed that the thermal properties of the composite ma-
terial are primarily determined by the polymer matrix,
while the contribution of the filler to heat transfer was not
explicitly considered. This assumption is justified by the fact
that polyethylene, as the dominant phase in the composite,
largely determines the overall thermal behavior of the ma-
terial.
The temperature excesses of the solar cell and the CPCF are
defined as:
𝜃𝑠(𝑡) = 𝑇𝑠(𝑡) − 𝑇𝑎(𝑡) (3)
𝜃𝑝(𝑡) = 𝑇𝑝(𝑡) − 𝑇𝑎(𝑡) (4)
where 𝑇𝑠 and 𝑇𝑝 are the temperatures of the solar cell and
CPCF, respectively; while 𝑇𝑎 is the ambient temperature.
The ambient temperature is approximated as a sinusoidal
function of time:
𝑇𝑎(𝑡) = 𝐴𝑡𝑒𝑚𝑝𝑠𝑖𝑛 (
2𝜋
24
𝑡 + 𝑡𝑠ℎ𝑖𝑓𝑡) (5)
where 𝐴𝑡𝑒𝑚𝑝 is the amplitude of temperature variation,
and 𝑡𝑠ℎ𝑖𝑓𝑡 accounts for phase shifts in the daily temperature
cycle.
This model is characterized by the following parameters:
• Geometric dimensions: surface areas 𝑆𝑠 and 𝑆𝑝 with
corresponding thicknesses 𝑙𝑠 and 𝑙𝑝.
• Material properties: densities 𝜌𝑠 and 𝜌𝑝, and specific
heat capacities 𝑐𝑝𝑠 and 𝑐𝑝𝑝.
• Thermal characteristics: convective heat transfer coef-
ficients ℎ𝑠 and ℎ𝑝, solar absorption coefficient 𝐴𝑠, and
interfacial thermal contact resistance 𝑅𝑠𝑝.
Equations (1) and (2) can be rewritten as:
𝑑𝜃𝑠(𝑡)
𝑑𝑡
=
1
𝛼𝑠
(𝛽𝑠𝑞(𝑡) − 𝛾𝑠𝜃𝑠(𝑡) + 𝛿𝑠𝜃𝑝(𝑡)) (6)
𝑑𝜃𝑝(𝑡)
𝑑𝑡
=
1
𝛼𝑝
(𝑃(𝑡) − 𝛾𝑝𝜃𝑝(𝑡) + 𝛿𝑝𝜃𝑠(𝑡)) (7)
where:
𝛼𝑠 = 𝑆𝑠𝜌𝑠𝑐𝑝𝑠𝑙𝑠;
𝛽𝑠 = 𝑆𝑠𝐴𝑠;
𝛾𝑠 = 𝑆𝑠ℎ𝑠 +
1
𝑅𝑠𝑝
;
𝛿𝑠 =
1
𝑅𝑠𝑝
;
𝛼𝑝 = 𝑆𝑝𝜌𝑝𝑐𝑝𝑝𝑙𝑝;
𝛾𝑝 = 𝑆𝑝ℎ𝑝 +
1
𝑅𝑠𝑝
and 𝛿𝑝 =
1
𝑅𝑠𝑝
.
To describe the process of the CPCF's influence on the SC,
a model of power dissipation and percolation conductivity
is presented. It is based on the assumption that the power
dissipation in the CPCF is determined by the short-circuit
photocurrent 𝐼𝑠𝑐 and the fuse’s temperature-dependent
resistance 𝑅𝑝 according to Joule’s heating law:
𝑃(𝑡) = 𝐼𝑠𝑐
2 ∗ 𝑅𝑝 (8)
The resistance of the CPCF depends on its thickness, cross-
sectional area, and conductivity:
𝑅𝑝 =
𝑙
𝜎(𝑇𝑝)∗𝑆𝑐𝑠
(9)
where: 𝜎(𝑇𝑝) is the conductivity of the CPCF, which can be
obtained from the percolation theory of conductance for
materials that undergo a metal-dielectric transition [14]:
{
𝜎(∆𝑇𝑝) = 𝐴 ∗ 𝑒𝑥𝑝
−∆𝐸
𝑘𝑇𝑝 (
𝑉𝑓(∆𝑇𝑝)−𝑉𝑐
1−𝑉𝑐
)
𝑡
, 𝑇𝑝 < 𝑇𝑐
𝜎(∆𝑇𝑝) = 𝜎𝑚 (
𝐴∗𝑒𝑥𝑝
−∆𝐸
𝑘𝑇𝑝
𝜎𝑚
)
𝑠
, 𝑇𝑝 = 𝑇𝑐
𝜎(∆𝑇𝑝) = 𝜎𝑚 (
𝑉𝑐−𝑉𝑓(∆𝑇𝑝)
𝑉𝑐
)
−𝑞
, 𝑇𝑝 > 𝑇𝑐
(10)
where: ∆𝑇𝑝 = 𝑇𝑝 − 𝑇0, and 𝑇0 is the initial ambient temper-
ature; 𝑉𝑓 is the volume fraction of a filler:
𝑉𝑓(∆𝑇𝑝) =
1
1 +
(1 − 𝑉𝑓0)(1 + 𝛽𝑚∆𝑇𝑝)
𝑉𝑓0(1 + 𝛽𝑓∆𝑇𝑝)
(11)
where: 𝑉𝑓0 is the volume of a filler at initial conditions, and
𝛽𝑓 and 𝛽𝑚 are the coefficients of thermal expansion of the
filler and matrix, respectively. 𝑇𝑐 is the critical temperature
of phase transition, determined from the equality
𝑉𝑓(∆𝑇𝑝) = 𝑉𝑐 . The constants 𝑡, 𝑠, 𝑞, and ∆𝐸 depend on the
fuse material properties [13].
An important component of approximation is the effect of
variable solar irradiance. According to the formula derived
in [15], the introduced distribution is expressed through the
duration of the local day 𝑡𝑑 and the maximum values of the
daily received irradiance 𝑞𝑚𝑎𝑥 . Solar radiation on a hori-
zontal surface depends on the degree of symmetry relative
to the point 𝑡 = 𝑡𝑚𝑎𝑥, at which the received solar irradi-
ance reaches its maximum values. In the developed math-
ematical model, the distribution is assumed to be symmet-
ric around the point 𝑡𝑚𝑎𝑥 =
𝑡𝑑
2
, which leads to the following
expression:
𝑞(𝑡) = 𝑞𝑚𝑎𝑥 (
𝑡
𝑡𝑚𝑎𝑥
)
2
(
𝑡𝑑 − 𝑡
𝑡𝑑 − 𝑡𝑚𝑎𝑥
)
2
(12)
The length of the day 𝑡𝑑 can be approximated in terms of
latitude 𝜑 and the solar declination angle 𝛿 as follows:
𝑡𝑑 =
24
180°
𝑎𝑟𝑐𝑐𝑜 𝑠(𝑡𝑎𝑛𝜑 𝑡𝑎𝑛𝛿) (13)
and formula for solar inclination angle is:
𝛿 = 23.45𝑠𝑖𝑛360 (
284 + 𝑛
365
) (14)
Here, 𝑛 is the day of the year starting from January 1st.
An integral part of the mathematical model is the inclusion
of a description for determining the temperature-depend-
ent photovoltaic characteristics for calculating the power
118
Відновлювана енергетика. № 3/2025 | Сонячна енергетика
generation of solar energy. The mathematical model em-
ploys a dependence that describes the short-circuit current
density of the solar cell as a function of the solar cell tem-
perature and solar irradiance [16]:
𝐽𝑠𝑐 = 𝑒 ∗ 𝑄(1 − 𝑅𝑐(𝑇𝑠))(1 − 𝑒𝑥𝑝
−𝜇𝑙)
𝑞(𝑡)
𝐸𝑔
(15)
where: elementary charge is denoted by e, and Q repre-
sents the collection factor of the solar cell. The reflection
coefficient of the front surface of the solar cell, 𝑅𝑐, is given
by the equation:
𝑅𝑐(𝑇𝑠) = 0.322 + 3.12 ∗ 10−5𝑇𝑠 (16)
where: 𝑇𝑠 is the absolute temperature of the surface of the
solar cell (under zero gradient conditions); μ is the attenu-
ation coefficient, and the value is given as:
𝜇 = 𝑎𝑒
𝑇𝑠
𝜏 (17)
where 𝑎 = 3.17 × 104 and 𝜏 = 346𝐾. The variable 𝑙 (in
meters) represents the thickness of the solar cell [16].
The energy band gap for the semiconductor is given as [16]:
𝐸𝑔 = 𝐸𝑔(0) −
𝛼𝑇𝑠
2
𝑇𝑠 + 𝛽
(18)
For silicon: 𝐸𝑔(0) = 1.16𝑒𝑉, 𝛼 = 7 × 10−14𝑒𝑉 ∙ 𝐾−1 and
𝛽 = 1100𝐾.
The open circuit voltage 𝑉𝑜𝑐 is defined as [16]:
𝑉𝑜𝑐 =
𝐾𝑇𝑠
𝑒
𝑙𝑛 (
𝐽𝑠𝑐
𝐽0
+ 1) (19)
where: the Boltzmann constant is denoted by K, and e rep-
resents the elementary charge. The reverse saturation cur-
rent density, 𝐽0 , depends on temperature as follows [15]:
𝐽0 = 𝜀𝑛𝑇𝑠
𝛾𝑒𝑥 𝑝 (
−𝐸𝑔
𝐾𝑇𝑠
) (20)
where ε = 179
𝐴
𝐾3𝑚2 for a silicon solar cell; 𝑛 is a non-ideal-
ity factor taken as 𝑛 = 1, and 𝛾 = 3 [15].
The silicon solar cell is considered with dimensions of
156mm × 156mm × 3.5mm.
The solar absorption coefficient 𝐴𝑠 is taken as 0.8. Convec-
tive heat transfer coefficients for both SC and CPCF are
taken as ℎ𝑠 = ℎ𝑝 = 20
𝑊
𝑚2𝐾
. The density and specific heat
capacity of silicon are:
𝜌𝑠 = 2280
𝑘𝑔
𝑚3, 𝑐𝑝𝑠 = 840
𝐽
𝑘𝑔∗𝐾
.
The distribution of diurnal solar radiation is considered for
Stony Brook, New York, as an example. For Stony Brook on
September 3, the corresponding parameters for estimating
solar radiation distribution are: 𝑞𝑚𝑎𝑥 = 850
𝑊
𝑚2, 𝑛 = 245,
φ = 40.9257°.
The length of the local daytime is approximated to be 𝑡𝑑 ≈
12.5ℎ , and the time corresponding to maximum solar radi-
ation is 𝑡𝑚𝑎𝑥 = 6.25 ℎ. The amplitude of the ambient
temperature variation is taken as 𝐴𝑡𝑒𝑚𝑝 = 12°C, while the
time shift is considered to be 0.
The presence of CPCF in the electrical circuit should not af-
fect the normal operation of the system. Therefore, there
are two requirements for CPCF selection [10]: the internal
resistance of the solar cell 𝑟 must be significantly higher
than the minimal initial resistance of the CPCF, i.e., r ≫
𝑅𝑚𝑖𝑛; the short-circuit current of the solar cell must not ex-
ceed the triggering current 𝐼𝑡𝑟𝑖𝑝 of the CPCF, i.e., 𝐼𝑡𝑟𝑖𝑝 > 𝐼𝑠𝑐 .
The volume fraction of the filler 𝑉𝑓0 at initial conditions is
0.23, while the critical volume fraction 𝑉𝑐 is 0.14. This re-
sults in a critical temperature of the CPCF 𝑇𝑐 = 114°C.
Percolation exponents were assigned as follows: 𝑠 = 0.62,
and 𝑞 = 1 [10].
The thermal expansion coefficients of the polyethylene ma-
trix and the filler were:
𝛽𝑚 = 6.93 × 10⁻³ K⁻¹ , 𝛽𝑓 = 10⁻⁶ K⁻¹ , respectively [13].
Additionally, the thermal conductivity of the matrix was
given as 𝜎𝑚 = 5 × 10⁻¹⁴
𝑊
𝑚∗𝐾
.
The computations were performed using Python within the
PyCharm integrated development environment. The sys-
tem of differential equations was numerically solved using
the backward differentiation formula (BDF) method from
the scipy.integrate library. The BDF method was chosen
due to the stiffness of the first-order differential equations
in this study, ensuring solution stability.
To compute the area between curves, the composite Simp-
son’s rule was applied, providing a reasonable approxima-
tion. This was implemented using the Simpson function
from scipy.integrate.
The simulations analyze the thermal response of the CPCF-
integrated solar cell under varying diurnal sunlight condi-
tions, considering factors such as ambient temperature
fluctuations, power dissipation, and solar irradiance distri-
bution. The results show the temperature dynamics of both
the solar cell and the CPCF. Additionally, the total power
output of the system, power generated by the solar cell,
and power dissipated on the CPCF are calculated for differ-
ent values of contact thermal resistance (𝑅𝑠𝑝), and various
CPCF material properties such as: preexponential coeffi-
cient 𝐴, activation energy ∆𝐸, percolation transition expo-
nent 𝑡, and thickness 𝑙𝑝.
First, simulations were conducted with four different val-
ues of thermal resistance 𝑅𝑠𝑝 to analyze the thermal behav-
ior of the system. The corresponding CPCF material proper-
ties were applied and held constant, including the
percolation exponent 𝑡 = 1.2 for the metal-conductive
state of CPCF, the pre-exponential coefficient 𝐴 = 1200 in
the metal-conductive state, and the activation energy
∆𝐸 = 9.72 × 10−21 J. Additionally, the CPCF layer thick-
ness was set to 𝑙𝑝 = 0.002𝑚 . Equation (21) was used to
calculate the energy loss.
𝐸𝑙𝑜𝑠𝑠 = ∫ 𝑃𝑔𝑒𝑛𝑑𝑡
𝑡𝑑
0
−∫ 𝑃𝑡𝑜𝑡𝑎𝑙𝑑𝑡 (21)
𝑡𝑑
0
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Table 1 presents a comparison of the results obtained for
four different values of thermal contact resistance: 0.1
°𝐶
𝑊
,
0.5
°𝐶
𝑊
, 1.0
°𝐶
𝑊
, and 1.5
°𝐶
𝑊
. Knowing the temperatures of
both CPCF and SC at each point in time enabled the
calculation of solar cell power generation and power dissi-
pation in CPCF.
To illustrate the temperature dynamics for different ther-
mal contact resistance values, Fig. 1 was generated based
on solved differential equations.
Table 1. Temperature and power distributions for 4 different values of contact thermal resistance 𝑹𝒔𝒑
Parameter 𝑹𝒔𝒑 = 0.1
°𝑪
𝑾
𝑹𝒔𝒑 = 0.5
°𝑪
𝑾
𝑹𝒔𝒑 = 1.0
°𝑪
𝑾
𝑹𝒔𝒑 = 1.5
°𝑪
𝑾
𝑇𝑠 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑇𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
Total Energy Generation, 𝐸𝑔𝑒𝑛 (Wh) To-
tal Energy Loss, 𝐸𝑙𝑜𝑠𝑠 (Wh)
Total System Output, 𝐸𝑡𝑜𝑡𝑎𝑙 (Wh)
41.4
40.6
26.3
1.7
24.6
42.8
39.1
26.2
1.7
24.5
44.3
37.7
26.2
1.8
24.4
45.5
36.4
26.1
1.7
24.4
Fig. 1. Temperature dynamics for different values of contact thermal resistance (𝑅𝑠𝑝) between layers of SC and CPCF.
(a) 𝑅𝑠𝑝 = 0.1
°𝐶
𝑊
, (b) 𝑅𝑠𝑝 = 1.0
°𝐶
𝑊
Next, the power output analysis of the model was con-
ducted based on 4 varying thickness values: 1mm, 2mm,
3mm, 4mm. The results are shown in Table 2. The corre-
sponding simulation parameters included thermal contact
resistance 𝑅𝑠𝑝 = 0.5
°𝐶
𝑊
, exponent 𝑡 = 1.2 for the metal-
conductive state of CPCF, pre-exponential coefficient 𝐴 =
1200 in the metal-conductive state, and activation energy
∆𝐸 = 9.72 × 10−21 J.
Lastly, a variety of material constants were examined. Fig. 2
illustrates the dependence of CPCF resistance on tempera-
ture for two different values of percolation exponent 𝑡
(equation 10). Graphs were obtained for a logarithmic scale
of resistance.
For this simulation, thermal contact resistance 𝑅𝑠𝑝 was set
to 0.5
°𝐶
𝑊
, pre-exponential coefficient 𝐴 = 1200, activation
energy ∆𝐸 = 9.72 × 10−21 J and CPCF layer thickness 𝑙𝑝 =
0.002𝑚. Four different values of the percolation transition
exponent 𝑡 were studied. The percolation exponent plays a
crucial role in defining how conductivity changes as the
filler concentration approaches the percolation threshold.
By varying 𝑡, it is possible to assess the sensitivity of the
system’s power distribution to changes in the conductive
network structure. Table 3 illustrates how four different
values of 𝑡 affect the power distribution of the system.
Fig. 3 illustrates the power distribution for two different
values of the percolation transition exponent 𝑡.
Table 2. Temperature and power distributions for 4 different values of CPCF thickness 𝒍𝒑
Parameter 𝒍𝒑 = 0.001m 𝒍𝒑 = 0.002m 𝒍𝒑 = 0.003m 𝒍𝒑 = 0.004m
𝑇𝑠 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑇𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
Total Energy Generation, 𝐸𝑔𝑒𝑛 (Wh) To-
tal Energy Loss, 𝐸𝑙𝑜𝑠𝑠 (Wh)
Total System Output, 𝐸𝑡𝑜𝑡𝑎𝑙 (Wh)
42.8
39.2
30.0
1.9
28.1
42.8
39.1
30.0
3.9
26.1
42.8
39.1
30.0
5.8
24.2
42.8
39.1
30.0
7.8
22.2
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Fig. 2. Variation of the CPCF resistance as a function of temperature for two values of 𝑡. (a) 𝑡 = 1.0, (b) 𝑡 = 1.6
Table 3. Temperature and power distributions for 4 different values of percolation transition exponent t
Fig. 3. Power distribution at the system throughout the solar hours for two values of 𝑡. (a) 𝑡 = 1.0, (b) 𝑡 = 1.6
For the following simulation, the thermal contact re-
sistance 𝑅𝑠𝑝 was set to 0.5
°𝐶
𝑊
, the activation energy ∆𝐸 =
9.72 × 10−21 J, percolation transition exponent 𝑡 = 1.2,
and the CPCF layer thickness 𝑙𝑝 = 0.002𝑚. The pre-expo-
nential coefficient 𝐴 was varied across multiple values to
study its effect on the system’s power distribution. The pre-
exponential factor, commonly denoted as 𝐴, serves as a co-
efficient in the percolation theory conductivity equation,
which characterizes how the preexponential factor relates
directly to the frequency of successful collisions between
charge carriers in the conductive network. Table 4 presents
the impact of different values of 𝐴 on the power
distribution of the system, illustrating how variations in this
parameter affect thermal and electrical performance.
Then, different values of CPCF activation energy were stud-
ied. The thermal contact resistance 𝑅𝑠𝑝 was set to 0.5
°𝐶
𝑊
,
pre-exponential coefficient 𝐴 = 1200, percolation transi-
tion exponent 𝑡 = 1.2, and the CPCF layer thickness 𝑙𝑝=
0.002m. The activation energy ∆𝐸 was varied across multi-
ple values to study its effect on the system’s power distri-
bution. The activation energy of a CPCF is the minimum
thermal energy required to initiate a significant increase in
the material’s electrical resistance due to the disruption of
the conductive network within the polymer matrix. This
Parameter 𝒕 = 1.0 𝒕 = 1.2 𝒕 = 1.4 𝒕 = 1.6
𝑇𝑠 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑇𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑅𝑝 at 𝑡 = 0 (Ω)
𝑅𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (Ω)
Total Energy Generation, 𝐸𝑔𝑒𝑛 (Wh) To-
tal Energy Loss, 𝐸𝑙𝑜𝑠𝑠 (Wh)
Total System Output, 𝐸𝑡𝑜𝑡𝑎𝑙 (Wh)
42.8
39.1
0.010
0.012
30.0
2.2
27.8
42.8
39.2
0.018
0.021
30.0
3.9
26.1
42.8
39.2
0.29
0.037
30.0
6.9
23.1
42.8
39.2
0.050
0.067
30.0
12.2
17.8
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Відновлювана енергетика. № 3/2025 | Сонячна енергетика
energy corresponds to the temperature-dependent pro-
cesses such as polymer expansion, filler debonding, or
phase transitions driving the material from a conductive
into a high-resistance (fused) state.
Table 4. Temperature and power distributions for 4 different values of percolation pre-exponential coefficient A
Table 5 presents the temperature and power distribution
of the system with varying values of activation energy ∆𝐸.
The numerical simulations revealed several important in-
sights regarding the influence of key parameters on system
performance, which are discussed in detail below.
Thermal contact resistance (𝑅𝑠𝑝) at the interface between
a solar cell and a polymer composite layer is influenced by
multiple factors, including surface roughness, contact pres-
sure, material properties, and interfacial air gaps [17]. The
range of 0.1 − 1.5
°𝐶
𝑊
used in this study appropriately in-
cludes both ideal conditions (lower 𝑅𝑠𝑝 values) and more
challenging interface scenarios (higher 𝑅𝑠𝑝 values) that
might occur in practical applications. This range allows for
comprehensive analysis of how thermal contact resistance
affects temperature distribution and system performance
across various manufacturing and installation conditions,
providing valuable insights for optimizing the thermal de-
sign of CPCF-integrated SCs.
Table 5. Temperature and power distributions for 4 different values of CPCF activation energy ∆𝑬
Discussions
The thermal contact resistance (𝑅𝑠𝑝) between the solar cell
and CPCF layers significantly impacts the temperature distri-
bution within the system. As shown in (Table 1), increasing
𝑅𝑠𝑝 from 0.1
°𝐶
𝑊
to 1.5
°𝐶
𝑊
resulted in higher solar cell temper-
atures (from 41.4°C to 45.5°C at maximum solar radiation)
and lower CPCF temperatures (from 40.6°C to 36.4°C). This
temperature change is critical for the proper functioning of
the protection mechanism, as it determines how effectively
heat is transferred from the solar cell to the CPCF layer. In
other words, it defines the sensitivity of the CPCF.
The further analysis of thermal contact resistance (𝑅𝑠𝑝) re-
veals that while lower 𝑅𝑠𝑝 values result in higher CPCF tem-
peratures, this temperature difference has a negligible ef-
fect on power dissipation and overall system performance.
The energy loss remains nearly constant (1.7 − 1.8Wh)
across all 4 cases. Therefore, increasing 𝑅𝑠𝑝 to reduce
power dissipation on the CPCF appears unnecessary, as the
thermal efficiency gains would be minimal. Instead, 𝑅𝑠𝑝
should be optimized primarily for protection sensitivity.
The temperature dynamics illustrated in Fig. 1 further
demonstrate that higher thermal contact resistance cre-
ates a more pronounced temperature difference between
the solar cell and CPCF. This characteristic could be advan-
tageous in applications where a delayed response from the
protection mechanism is desired, allowing for current to
flow through without triggering the fuse. Conversely, in ap-
plications requiring rapid response to hot spots, lower ther-
mal contact resistance would be preferable.
The thickness of the CPCF layer (𝑙𝑝) emerged as a critical
parameter affecting the system’s electrical performance.
As shown in Table 2, increasing the CPCF thickness from
1mm to 4mm had a dramatic effect on energy losses, which
increased from 1.9Wh to 7.8Wh. Consequently, the total
system output decreased significantly from 28.1Wh to
22.2Wh, representing a reduction of approximately 21 per-
cent. This substantial impact on system performance can
Parameter 𝑨 = 250 𝑨 = 500 𝑨 = 900 𝑨 = 1200
𝑇𝑠 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑇𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑅𝑝 at 𝑡 = 0 (Ω)
𝑅𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (Ω)
Total Energy Generation, 𝐸𝑔𝑒𝑛 (Wh) To-
tal Energy Loss, 𝐸𝑙𝑜𝑠𝑠 (Wh)
Total System Output, 𝐸𝑡𝑜𝑡𝑎𝑙 (Wh)
42.8
39.1
0.077
0.101
30.0
18.8
11.1
42.8
39.1
0.042
0.050
30.0
9.4
20.6
42.8
39.1
0.023
0.028
30.0
5.2
24.8
42.8
39.1
0.018
0.021
30.0
3.9
26.1
Parameter
∆𝑬 = 4.80×
𝟏𝟎−𝟐𝟏J
∆𝑬 = 9.72×
𝟏𝟎−𝟐𝟏J
∆𝑬 = 12.8×
𝟏𝟎−𝟐𝟏J
∆𝑬 = 16.2×
𝟏𝟎−𝟐𝟏J
𝑇𝑠 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑇𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (°C)
𝑅𝑝 at 𝑡 = 0 (Ω)
𝑅𝑝 at 𝑡 = 𝑡𝑚𝑎𝑥 (Ω)
Total Energy Generation, 𝐸𝑔𝑒𝑛 (Wh)
Total Energy Loss, 𝐸𝑙𝑜𝑠𝑠 (Wh)
Total System Output, 𝐸𝑡𝑜𝑡𝑎𝑙 (Wh)
42.8
39.1
0.005
0.007
30.0
1.2
28.8
42.8
39.1
0.018
0.021
30.0
3.9
26.1
42.8
39.1
0.037
0.043
30.0
8.1
21.9
42.8
39.1
0.082
0.091
30.0
17.4
12.6
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Відновлювана енергетика. № 3/2025 | Сонячна енергетика
be attributed to the increased electrical resistance of
thicker CPCF layers, as resistance is directly proportional to
length according to equation (9). The increased resistance
leads to higher power dissipation during normal operation,
reducing the overall efficiency of the system. The tempera-
ture behavior of both the solar cell and CPCF remained un-
changed across different thickness values. This indicates
that while thickness significantly affects electrical perfor-
mance, its impact on thermal behavior is minimal under
normal operating conditions of the CPCF. This finding sug-
gests that CPCF thickness should be minimized to reduce
energy losses while maintaining adequate protection capa-
bilities.
While the numerical simulations in this study suggest that
the most effective conductive polymer composite fuses for
protecting 156 × 156mm solar cell wafers are approxi-
mately 1mm thick, the current manufacturing standards
present a significant challenge. As demonstrated in Table 6
[18, 19, 20], commercial fuses, that satisfy fuse selection
requirements for 156 x 156mm solar cell wafers established
in the study [10], from leading manufacturers such as Lit-
telfuse, Bourns, and Fuzetec typically range from 3.0 to
4.0mm in thickness, which is substantially thicker than the
theoretically optimal size. This issue highlights a critical gap
between theoretical optimization and current manufactur-
ing capabilities. The thicker fuses, while readily available,
may introduce additional energy losses and thermal ineffi-
ciencies that could compromise the overall performance of
the solar cell protection system. However, it should be
mentioned that the increased thickness of fuses from
prominent manufacturers is not only due to the active fuse
material but is also influenced by protective external shells
and packaging requirements. Still, the findings show the
need for advanced manufacturing techniques and material
innovations that can produce thinner fuses identified as op-
timal in this study.
Table 6. Examples of fuse parameters that satisfy requirements for 156x156 mm solar cells [10]
The percolation transition exponent 𝑡 plays a crucial role in
determining the temperature-dependent resistance char-
acteristics of the CPCF. As illustrated in Fig. 2, higher values
of 𝑡 result in steeper resistance-temperature increase
when the volume of the filler is higher than the percolation
threshold, indicating greater sensitivity to temperature
changes. This parameter influences how the conductive
network within the polymer-composite responds to ther-
mal variations. Our simulations showed that increasing 𝑡
from 1.0 to 1.6 increased energy losses from 2.2Wh to
12.2Wh, resulting in a reduction in total system output
from 27.8Wh to 17.8Wh (Table 3). This represents a de-
crease of approximately 36 percent in system efficiency.
The power distribution curves shown in Figure 3 further il-
lustrate that higher 𝑡 values lead to increased power dissi-
pation in the CPCF throughout the day. This behavior can
be attributed to the more pronounced resistance increase
with temperature at higher 𝑡 values, resulting in greater
Joule heating losses during normal operation. Materials
with lower percolation transition exponents are preferable
for CPCF applications in SCs, as they minimize energy losses
during normal operation of the fuse.
The pre-exponential coefficient 𝐴 in the percolation theory
conductivity equation significantly influences the baseline
conductivity of the CPCF. Our simulations demonstrated
that increasing 𝐴 from 250 to 1200 reduced the initial re-
sistance (𝑅𝑚𝑖𝑛) from 0.077Ω to 0.018Ω (Table 4), resulting
in substantially lower energy losses (from 18.8Wh to
3.9Wh) and higher total system output (from 11.2Wh to
26.1Wh). This improvement in system performance with
higher 𝐴 values can be attributed to the reduced resistance
of the CPCF, which minimizes power dissipation during nor-
mal operation. The pre-exponential coefficient determines
the density of conductive pathways within the polymer ma-
trix, with higher values indicating more efficient charge
transport mechanisms. Materials with optimized filler dis-
persion and enhanced interfacial interactions between the
conductive filler and polymer matrix, exhibiting higher 𝐴
values, are promising candidates for this application.
The activation energy ∆𝐸 of the CPCF material defines the
temperature sensitivity of its conductivity. Our simulations
showed that increasing ∆𝐸 from 4.80 × 10−21 J (0.03eV) to
16.1 × 10−21 J (0.1eV) resulted in a substantial increase in
initial resistance from 0.005Ω to 0.082Ω (Table 5). This led
to dramatically higher energy losses (from 1.2Wh to
17.4Wh) and reduced total system output (from 28.8Wh to
12.6Wh), representing a decrease of approximately 56 per-
cent. The significant impact of activation energy on system
Manufacturer Model Thickness (mm) Trip Current (A) Minimal Resistance (Ω)
Littelfuse
16R1400G
30R900U
AGRF1400
3.0
3.0
3.5
23.8
18.0
27.3
0.0026
0.0050
0.0022
Bourns
MFRHS1200
MFRHT1300
MFRHS900
3.6
3.6
3.6
24.0
24.0
18.0
0.0035
0.0041
0.0046
Fuzetec
FRU900-30F
FRG1200-16F
FHE1000-32F
3.0
3.6
4.0
18.0
20.4
20.0
0.0050
0.0020
0.0060
123
Відновлювана енергетика. № 3/2025 | Сонячна енергетика
performance can be explained by its exponential relation-
ship with resistance. Higher activation energies result in
greater temperature dependence of resistance, leading to
increased power dissipation during normal operation as
ambient and operating temperatures fluctuate throughout
the day. These findings indicate that CPCF materials with
lower activation energies are preferable for minimizing en-
ergy losses during normal operation.
Conclusions
The results of this study have several implications for the
design and implementation of CPCF-based protection sys-
tems for solar cells. First, our findings highlight the im-
portance of careful material selection and optimization.
The electrical properties of the CPCF, particularly the per-
colation transition exponent, preexponential coefficient,
and activation energy, have significant effects on system
performance under normal conditions of operation (high-
conductivity state of the CPCF) and must be carefully se-
lected to balance protection capabilities with energy effi-
ciency.
Second, the thickness of the CPCF layer should be mini-
mized to reduce energy losses while maintaining adequate
protection. This may require the development of novel
manufacturing techniques capable of producing thin, uni-
form CPCF layers with consistent properties.
Third, the thermal contact resistance between the solar cell
and CPCF layers should be optimized based on the specific re-
quirements of the application. Lower thermal contact re-
sistance may be preferable for applications requiring rapid re-
sponse to hot spots, without compromising system efficiency.
Future research should focus on experimental validation of
these numerical findings, particularly under hot spot condi-
tions. Additionally, the development of CPCF materials with
optimized properties for solar cell protection applications
represents a promising field for future work. Finally, the in-
tegration of CPCF layers into commercial solar panels and
the evaluation of their long-term reliability and perfor-
mance under real-world conditions should be investigated.
In conclusion, this study provides insights into the thermal
and electrical behavior of solar cells integrated with CPCF
protection layers under varying diurnal sunlight conditions.
The findings contribute to the development of more effi-
cient and reliable solar energy systems by analyzing the key
parameters affecting the performance of CPCF-based pro-
tection mechanisms.
REFERENCES
1. Ember. (2024). Global electricity review 2024.
https://ember-energy.org/latest-insights/global-elec-
tricity-review-2024/
2. International Energy Agency Photovoltaic Power Sys-
tems Programme (IEA PVPS). (2014). Review of failures
of photovoltaic modules: International Energy Agency
PVPS Task 13.
3. Zhang, Z., Wang, L., et al. (2016). Study of bypass diode
reliability under non-uniform irradiance distribution on
PV module surface. Acta Energiae Solaris Sinica, 37(2),
355–360.
4. Fonseca Batista, R. V. (2018). The impact of shadowing
in photovoltaic systems and how to minimize it: An
analysis with the PVSyst software. https://www.diva-
portal.org/smash/get/diva2:1214973/FULLTEXT01.pdf
5. Sullivan, R. M. (1965). Shadow effects on a series-paral-
lel array of solar cells (NASA Technical Memorandum
NASA-TM-X-55269). NASA Goddard Space Flight Center.
https://ntrs.nasa.gov/api/cita-
tions/19650016433/downloads/19650016433.pdf
6. Vieira, R. G., de Araújo, F. M. U., Dhimish, M., & Guerra,
M. I. S. (2020). A comprehensive review on bypass diode
application on photovoltaic modules. Energies, 13(10),
2472. https://doi.org/10.3390/en13102472
7. d’Alessandro, V., Guerriero, P., & Daliento, S. (2013). A
simple bipolar transistor-based bypass approach for
photovoltaic modules. IEEE Journal of Photovoltaics,
4(1), 405–413.
8. Guerriero, P., Tricoli, P., & Daliento, S. (2019). A bypass
circuit for avoiding the hot spot in PV modules. Solar En-
ergy, 181, 430–438.
9. Tonkoshkur, A. S., Ivanchenko, A. V., Nakashydze, L. V.,
Lyashkov, A. Yu., & Gomilko, V. (2021). Application of
polymer posistor nanocomposites in systems for pro-
tecting photovoltaic components of solar arrays from
electrical overloads. Primedia eLaunch.
10. Lyashkov, A. Yu., Makarov, V. O., & Plakhtii, Y. G. (2022).
Modeling of resettable fuses characteristics for protection
of solar arrays from current overloads. Multidiscipline
Modeling in Materials and Structures, 18(2), 328–338.
11. Tonkoshkur, A. S., Ivanchenko, A. V., Nakashydze, L. V.,
Lyashkov, A. Yu., & Gomilko, V. (2019). Posistor ele-
ments based on ceresin–nanocarbon composites. Jour-
nal of Physics and Electronics, 27(1), 71–78.
12. Tonkoshkur, A. S., & Ivanchenko, A. V. (2020). Modelling
of overheating in solar photovoltaic cell plates with lo-
cal electric heat sources. Journal of Physics and Elec-
tronics, 28(1), 77–84.
13. Zainutdinov, A. Kh., Kasymov, A. A., Alimov, R. A., & Ma-
grupov, M. A. (1994). Influence of thermal expansion on
the conductivity of polymer conducting composites.
Journal of Engineering Physics and Thermophysics,
66(3).
14. El-Adawi, M. K. (2019). Prediction of symmetrical and
asymmetrical global solar irradiance distribution—New
approach. Optical and Photo Journal, 9, 15–24.
15. Shaban, S. S. M. (2020). The solar cell parameters as a
function of its temperature in relation to its diurnal ef-
ficiency. Optics and Photonics Journal, 10, 1–12.
https://ntrs.nasa.gov/api/citations/19650016433/downloads/19650016433.pdf
https://ntrs.nasa.gov/api/citations/19650016433/downloads/19650016433.pdf
124
Відновлювана енергетика. № 3/2025 | Сонячна енергетика
16. Singh, P., & Ravindra, N. M. (2012). Temperature de-
pendence of solar cell performance—An analysis. Solar
Energy Materials and Solar Cells, 101, 36–45.
17. Gibbins, J. (2006). Thermal contact resistance of poly-
mer interfaces (Master’s thesis). University of Water-
loo, Ontario, Canada.
18. Littelfuse. (2025). Polyswitch resettable PPTC devices.
Retrieved from
https://www.littelfuse.com/products/fuses-overcur-
rent-protection/polyswitch-resettable-pptc-devices
19. “Multifuse Polymer PTC Resettable Fuses.” Bourns.
Retrived from www.bourns.com/products/circuit-pro-
tection/resettable-fuses-multifuse-pptc
20. “PPTC Resettable Fuse Product Catalog.” Fuzetec.
Retrived from www.fuzetec.com/upload/down-
load/Fuzetec%202021%20PPTC%20Catalog.pdf
https://www.littelfuse.com/products/fuses-overcurrent-protection/polyswitch-resettable-pptc-devices
https://www.littelfuse.com/products/fuses-overcurrent-protection/polyswitch-resettable-pptc-devices
http://www.bourns.com/products/circuitprotection/resettablefusesmultifusepptc
http://www.bourns.com/products/circuitprotection/resettablefusesmultifusepptc
http://www.fuzetec.com/upload/download/Fuzetec%202021%20PPTC%20Catalog.pdf
http://www.fuzetec.com/upload/download/Fuzetec%202021%20PPTC%20Catalog.pdf
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| id | veorgua-article-556 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:16:50Z |
| publishDate | 2025 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/78/410848b029a5023c624a498596cbb678.pdf |
| spelling | veorgua-article-5562026-07-18T06:32:22Z INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS ВПЛИВ ЕЛЕКТРОТЕПЛОВИХ ПАРАМЕТРІВ ПОЛІМЕРНИХ КОМПОЗИТНИХ ЗАПОБІЖНИКІВ НА ЕФЕКТИВНІСТЬ СОНЯЧНИХ ЕЛЕМЕНТІВ Korsunskyi , R. Nakashydze, L. solar cell, conductive polymer composite fuse, percolation, nanofiller, polymer matrix. сонячний елемент, електропровідний полімерно-композитний запобіжник, перколяція, наповнювач, полімерна матриця. A solar cell system integrated with a conductive polymer composite fuse (CPCF) for passive protection against hot spot formation was numerically investigated. The model, based on differential heat balance equations, simulates diurnal temperature and power dynamics for Stony Brook, NY, on September 3rd, when the fuse is in the high-conductivity state, by considering heat exchange between the solar cell and the CPCF under varying solar irradiance and ambient conditions. Key material and structural parameters—such as thermal contact resistance, CPCF thickness, activation energy, percolation pre-exponential factor, and transition exponent—are varied to evaluate their influence on system performance. Results demonstrate that thermal contact resistance significantly influences temperature distribution between components without substantially affecting power output, while electrical parameters such as activation energy and percolation constants significantly influence power dissipation and overall energy loss. The findings provide a framework for optimizing CPCF design to enhance solar cell reliability and efficiency, offering a cost-effective, passive alternative to conventional hotspot mitigation methods.&nbsp; Було чисельно досліджено сонячний елемент, інтегрований з провідним полімерно-композитним запобіжником для пасивного захисту від утворення гарячих точок. Математична модель, заснована на диференціальних рівняннях теплового балансу, моделює фізичні процеси в цій системі для Стоуні-Брук, штат Нью-Йорк, 3 вересня, коли запобіжник перебуває у стані високої провідності, враховуючи теплообмін між сонячною батареєю та запобіжником за змінної сонячної радіації та умов навколишнього середовища. Ключові параметри матеріалу та конструкції, як-от термічний контактний опір, товщина матеріалу запобіжника, енергія активації запобіжника, передекспоненціальний коефіцієнт перколяції та показник перколяційного переходу, змінюються, щоб оцінити, як запобіжник впливає на продуктивність системи. Результати демонструють, що термічний контактний опір суттєво впливає на розподіл температури між компонентами без істотного впливу на вихідну потужність, тоді як електричні параметри, як-от енергія активації та константи перколяції, суттєво впливають на розсіювання потужності та загальні втрати енергії. Отримані результати забезпечують основу для оптимізації конструкції запобіжників для підвищення надійності та ефективності сонячних елементів, пропонуючи економічно ефективну пасивну альтернативу звичайним методам захисту від впливу гарячих точок.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Institute of Renewable Energy National Academy of Sciences of Ukraine 2025-09-28 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/556 10.36296/1819-8058.2025.3(82).115-124 Vidnovluvana energetika ; No. 3(82) (2025): Scientific and applied Journal renewable energy ; 115-124 Возобновляемая энергетика; ##issue.no## 3(82) (2025): Scientific and applied Journal renewable energy ; 115-124 Відновлювана енергетика; № 3(82) (2025): Науково-прикладний журнал Відновлювана енергетика; 115-124 2664-8172 1819-8058 10.36296/1819-8058.2025.3(82) en https://ve.org.ua/index.php/journal/article/view/556/466 Copyright (c) 2025 R. Korsunskyi , L. Nakashydze https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | solar cell conductive polymer composite fuse percolation nanofiller polymer matrix. Korsunskyi , R. Nakashydze, L. INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS |
| title | INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS |
| title_alt | ВПЛИВ ЕЛЕКТРОТЕПЛОВИХ ПАРАМЕТРІВ ПОЛІМЕРНИХ КОМПОЗИТНИХ ЗАПОБІЖНИКІВ НА ЕФЕКТИВНІСТЬ СОНЯЧНИХ ЕЛЕМЕНТІВ |
| title_full | INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS |
| title_fullStr | INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS |
| title_full_unstemmed | INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS |
| title_short | INFLUENCE OF ELECTRO-THERMAL PARAMETERS OF POLYMER COMPOSITE FUSES ON THE EFFICIENCY OF SOLAR CELLS |
| title_sort | influence of electro-thermal parameters of polymer composite fuses on the efficiency of solar cells |
| topic | solar cell conductive polymer composite fuse percolation nanofiller polymer matrix. |
| topic_facet | solar cell conductive polymer composite fuse percolation nanofiller polymer matrix. сонячний елемент електропровідний полімерно-композитний запобіжник перколяція наповнювач полімерна матриця. |
| url | https://ve.org.ua/index.php/journal/article/view/556 |
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